The corresponding system of equations is consistent. The corresponding system
of equations is inconsistent. The rank of the augmented matrix is . The rank of
the augmented matrix is . The rank of the augmented matrix is . There are no
free variables. There is one free variable. There are two free variables. The
corresponding system has a unique solution. The corresponding system has
infinitely many solutions.
Consider the following augmented matrix in which denotes an arbitrary number and
denotes a nonzero number.
\begin{equation*} \left [ \begin{array}{ccccc|c} \blacksquare & \ast & \ast & \ast & \ast & \ast \\ 0 & \blacksquare & \ast & \ast & \ast & \ast \\ 0 & 0 & \blacksquare & \blacksquare & \ast & \ast \\ 0 & 0 & 0 & 0 & \blacksquare & 0 \end{array} \right ] \end{equation*}
Which of the following is true? Select all that apply.
Bibliography
This problem is based on Ken Kuttler, A First Course in Linear Algebra, Lyryx 2017, Open Edition, pp. 42–49.
2024-09-06 02:07:20